Mathematics

Problem

Statement-1 Let

\Delta_r = \begin{vmatrix} (r-1)! & n! \\ (r-1)^2 & (n!)^2 \\ (r-1)^3 & 3r^2 - 2n \end{vmatrix}, \text{ then } \prod_{r=2}^{n+1} \Delta_r = 0.

Statement-2

\prod_{r=1}^{n+1} \Delta_r = \Delta_2 \cdot \Delta_3 \cdot \Delta_4 \cdots \Delta_{n+1}